A Simple Design Example Realized a Full Eigenvalue Assignment and Partial Eigenvector Assignment Control That is Unrealizable by Other Existing Design Techniques

This example is the state space model of a 3-rd order system with two inputs and one output. Though very simple, it is well known that the 2×2 loop transfer function of this system cannot be even analyzed effectively by classical control theory, while the loop transfer function and robust property of state feedback control cannot be realized at all by the existing modern control design techniques for this system with more inputs than outputs. However, a comprehensive and fundamentally novel design technique very simply achieved superior performance and robustness for this system! A feature of this system example that it has one stable transmission zero is systematically and fully utilized, by designing an output feedback compensator (OFC) whose only pole matches that stable transmission zero. This OFC can realize a generalized state feedback control (GSFC) including its loop transfer function and robust properties. This GSFC is equivalent of the existing static output feedback control but with two outputs, and thus can assign all three poles and the sensitivity of one of the three poles. The new design technique used in this example is clearly very general, superior, and simple, and is clearly far more general, superior, and simple than the existing design techniques. It is a pity that this design technique is still largely unknown to the world control community. We all are witnessing who is good enough to recognize this momentous and seminal progress, and who is better to recognize this breakthrough sooner.